Ghost Imaging with Thermal Light: Comparing Entanglement and ClassicalCorrelation

We consider a scheme for coherent imaging that exploits the classical correlation of two beams obtained by splitting incoherent thermal radiation. This case is analyzed in parallel with the configuration based on two entangled beams produced by parametric down-conversion, and a precise formal analogy is pointed out. This analogy opens the possibility of using classical beams from thermal radiation for ghost imaging schemes in the same way as entangled beams.

Figure 1

Correlated imaging with incoherent thermal light. The thermal beam $a$ is splitinto two beams which travel through two distinct imaging systems. Arm 1includes an object. BS is a beam splitter, $D_1$ is a pointlike detector, $D_2$ is an array of pixel detectors, and $v$ is avacuum field.

Figure 2

Numerical simulation of the reconstruction of the diffraction patternof a phase double slit. $G({\overrightarrow{x}}_1=0,{\overrightarrow{x}}_2)$ after 80 000shots is shown for (a) entangled signal or idler beams from PDCand (b) classically correlated beams by splitting the idler beam.(c) is $\tilde{T}({\overrightarrow{x}}_2)$. Parameters arethose of a 4 mm $\beta$-barium-boratecrystal ($l_{\mathrm{c}\mathrm{o}\mathrm{h}}=16.6\mu \mathrm{m}$, ${\tau }_{\mathrm{c}\mathrm{o}\mathrm{h}}=0.97\mathrm{p}\mathrm{s}$). The pump waist and duration are $664\mu \mathrm{m}$ and1.5 ps. $x_0=\Delta q\lambda f/2\pi$.